Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <cstdio>

const int N = 200000 + 10;

int n, p[N], q[N], t[N], f[N];

int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &p[i]), q[p[i]] = i;
  for (int i = n - 1; i > 0; --i) {
    if (t[i + 1]) {
      int cnt = (q[f[i + 1]] < q[i]) + (q[i] < q[i + 1]) + (q[i + 1] < q[f[i + 1]]);
      if (cnt == 2) {
        t[i] = t[i + 1];
        f[i] = f[i + 1];
      } else {
        t[i] = t[i + 1] + 1;
        f[i] = i + 1;
      }
    } else if (q[i] > q[i + 1]) {
      t[i] = 1;
      f[i] = i + 1;
    }
  }
  printf("%d\n", t[1]);
  return 0;
}